Sharp non-asymptotic performance bounds for ℓ1 and Huber robust regression estimators
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Salvador Flores [1]
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[1] Universidad de Chile
Universidad de Chile
Santiago, Chile
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 24, Nº. 4, 2015, págs. 796-812
- Idioma: inglés
- DOI: 10.1007/s11749-015-0435-5
- Texto completo no disponible (Saber más ...)
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Resumen
A quantitative study of the robustness properties of the ℓ1 and the Huber M-estimator on finite samples is presented. The focus is on the linear model involving a fixed design matrix and additive errors restricted to the dependent variables consisting of noise and sparse outliers. We derive sharp error bounds for the ℓ1 estimator in terms of the leverage constants of a design matrix introduced here. A similar analysis is performed for Huber’s estimator using an equivalent problem formulation of independent interest. Our analysis considers outliers of arbitrary magnitude, and we recover breakdown point results as particular cases when outliers diverge. The practical implications of the theoretical analysis are discussed on two real datasets.
